Application of bootstrap method to evaluate bimodal data: an example of food microbiology proficiency test for sulfite-reducing anaerobes

Abstract

Statistical analysis has an essential role in proficiency test (PT) evaluation, especially when the distribution of results of the enumeration of microbiological bacteria is multimodal or strongly asymmetric, outliers aside. In these specific cases, the median or the robust mean of the PT results, calculated using the algorithm described in ISO 13528 Annex C, is not entirely appropriate for estimating the assigned value. A possible solution is to estimate the modes of kernel density function of data distribution and its uncertainty by using the nonparametric bootstrap technique. This method allows estimation of the sampling distribution of a statistic empirically without making assumptions about the form of the population. In the context of the PT for the enumeration of sulfite-reducing bacteria growing under anaerobic conditions organized in 2012 by QUAlity Assurance, although all participants used equivalent methods, the results showed high variability, which supported the hypothesis that two discrepant populations occurred in the test samples. When a bimodal distribution occurs, it is reasonable to suppose that at least one of the modes could be correct, but unless independent grounds for preferring one over the other are available, it is not possible to determine the assigned value and calculate the z-score. In the case of the sulfite-reducing bacteria PT, the true mode was not identified and the performance evaluation was not provided. For this reason, the PT provider (IZSVe) asked that the participants report every unusual situation for this test, should they occur during the next PTs. In this way, it may be possible to identify a plausible assigned value and its uncertainty as bootstrap mode of kernel density and standard error, respectively, and to provide the z-score as value of performance evaluation in the case of negligible uncertainty.